MODULE 7: DIGITAL FILTERS
TUTORIALS
(Note: Show all workings and explanations clearly)
1. a) Calculate the filter coefficients for a 5-tap FIR band pass filter with a lower cutoff
frequency of 2,000 Hz and an upper cutoff frequency of 2,400 Hz at a sampling rate of
8,000 Hz .
b) Compute and plot the magnitude and frequency response for
π π 3π
Ω=0 , , , ∧π rads .
4 2 2
ANSWER : b o=b 4=−0.09355 ,b 1=b3 =−0.01558∧b2=0.1
Magnitude frequency response:
2. a. Design a 5-tap FIR band reject filter with a lower cutoff frequency of 2,000 Hz , and an
upper cutoff frequency of 2,400 Hz, and a sampling rate of 8,000 Hz using the Hamming
window method.
b. Compute and plot the magnitude and frequency response for
π π 3π
Ω=0 , , , ∧π rads .
4 2 2
, ANSWER: b o=b 4=0.00748 , b1=b3=0.00841∧b2=0. 9
−1 −2 −3 −4
H ( z )=0.00748+0.00841 z + 0.9 z + 0.00841 z +0.00748 z
3. Given the FIR filter transfer function:
H ( z )=1+1.2 z −1 +0.36 z−2
Perform the FIR filter realization.
ANSWER:
4. Design a digital high pass Chebyshev filter with the following specifications:
a. 0.5 dB ripple on pass band at the frequency of 3, 000Hz
b. 25 dB attenuation at the frequency of 1,000Hz
c. Sampling frequency of 8,000Hz
d. Compute and plot the magnitude and frequency response for
π π 3π
Ω=0 , , , ∧π rads
4 2 2
0.1327−0.2654 z −1+ 0.1327 z −2
ANSWER: H ( z )= −1 −2
1+0.7996 z +0.3618 z
TUTORIALS
(Note: Show all workings and explanations clearly)
1. a) Calculate the filter coefficients for a 5-tap FIR band pass filter with a lower cutoff
frequency of 2,000 Hz and an upper cutoff frequency of 2,400 Hz at a sampling rate of
8,000 Hz .
b) Compute and plot the magnitude and frequency response for
π π 3π
Ω=0 , , , ∧π rads .
4 2 2
ANSWER : b o=b 4=−0.09355 ,b 1=b3 =−0.01558∧b2=0.1
Magnitude frequency response:
2. a. Design a 5-tap FIR band reject filter with a lower cutoff frequency of 2,000 Hz , and an
upper cutoff frequency of 2,400 Hz, and a sampling rate of 8,000 Hz using the Hamming
window method.
b. Compute and plot the magnitude and frequency response for
π π 3π
Ω=0 , , , ∧π rads .
4 2 2
, ANSWER: b o=b 4=0.00748 , b1=b3=0.00841∧b2=0. 9
−1 −2 −3 −4
H ( z )=0.00748+0.00841 z + 0.9 z + 0.00841 z +0.00748 z
3. Given the FIR filter transfer function:
H ( z )=1+1.2 z −1 +0.36 z−2
Perform the FIR filter realization.
ANSWER:
4. Design a digital high pass Chebyshev filter with the following specifications:
a. 0.5 dB ripple on pass band at the frequency of 3, 000Hz
b. 25 dB attenuation at the frequency of 1,000Hz
c. Sampling frequency of 8,000Hz
d. Compute and plot the magnitude and frequency response for
π π 3π
Ω=0 , , , ∧π rads
4 2 2
0.1327−0.2654 z −1+ 0.1327 z −2
ANSWER: H ( z )= −1 −2
1+0.7996 z +0.3618 z
